Discrete Models for Studying the Spread of Infectious Diseases: A Focus on Nt$$ {N}_t $$, Rt$$ {R}_t $$, and Transmission Scenarios

ABSTRACT Two discrete‐time models are presented for studying the spread of infectious diseases. The one‐dimensional model approximates the number of infected individuals , building on the work in [18]. The two‐dimensional model incorporates a mitigation function that depends on the effective reproduction number . Several contagion scenarios are explored, and applications are provided for COVID‐19 in Singapore and France, as well as a weak‐chaos analysis for Mexico City. The latter case includes the computation of the unstable manifold, offering a detailed view of the contagion dynamics. These results contribute to the understanding of contagion dynamics in different geographical settings and provide tools for prevention and decision‐making in the management of infectious diseases.